Find the measure of each marked angle. In Exercises 19–22, m and n are parallel. See Examples 1 and 2 .

Verified step by step guidance

1. Identify the given angles and their relationships with the parallel lines m and n.
2. Use the properties of parallel lines and transversals to determine the relationships between the angles. For example, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary.
3. Apply the appropriate angle relationship to set up an equation for the marked angles.
4. Solve the equation to find the measure of the marked angle.
5. Verify your solution by checking if the calculated angle satisfies the properties of parallel lines and transversals.

Key Concepts

Parallel Lines and Transversals

When two lines are parallel, and a transversal crosses them, several angle relationships are established. Corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary. Understanding these relationships is crucial for finding unknown angles formed by the intersection of parallel lines and a transversal.

Angle Relationships

In geometry, angles can be classified into various relationships such as complementary, supplementary, and vertical angles. Complementary angles sum to 90 degrees, while supplementary angles sum to 180 degrees. Recognizing these relationships helps in solving for unknown angles when given certain angle measures.

Angle Notation and Measurement

Angles are typically measured in degrees and can be represented using various notations, such as m∠A for the measure of angle A. Understanding how to interpret angle notation and measure angles accurately is essential for solving problems involving angles, especially in the context of parallel lines and transversals.